Decision variables

Xij = quantity shipped from supply region i to demand region j.

i = 1, 2, 3, 4 and j = 1, 2, 3, 4.

Yik = 1 if facility k is selected for supply region i; 0 otherwise,

where i = 1, 2, 3, 4 for each supply region; k = 1

(low capacity facility) or 2 (high capacity facility)

Future Plastics manufactures plastic products for industrial use worldwide. In order to meet demand, they are considering setting up a facility in each region in order to lower transportation dhsts and possibly avoid duties that could be imposed if the product is imported from another region. The disadvantage of this approach is that plants are sized to meet local demand and may not fully exploit economies of scale. Therefore, Future Plastics is also interested in determining the appropriate size of the facility to build in each location and is choosing between facilities with capacities of 5 or 10 million. Europe is critical for Future Plastic's development in the future. Hence, the company wants to ensure that either a low-capacity or a high facility capacity facility is built in the European supply region. If the high-capacity facility is built in South America, then high capacity must be built in North America as well. a. Define decision variables. Yow definition must include unit size \& time frame. b. Develop the Objective Function. c. Find the constraints. d. Use 'Excel - Solver' and find the optimal solution. (You must submit your excel work to get the full points.)